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As shown in the max-flow min-cut theorem, the weight of this cut equals the maximum amount of flow that can be sent from the source to the sink in the given network. In a weighted, undirected network, it is possible to calculate the cut that separates a particular pair of vertices from each other and has minimum possible weight.
A special case of constant weight codes are the one-of-N codes, that encode bits in a code-word of bits. The one-of-two code uses the code words 01 and 10 to encode the bits '0' and '1'. A one-of-four code can use the words 0001, 0010, 0100, 1000 in order to encode two bits 00, 01, 10, and 11.
The definition of an A p weight and the reverse Hölder inequality indicate that such a weight cannot degenerate or grow too quickly. This property can be phrased equivalently in terms of how much the logarithm of the weight oscillates: (a) If w ∈ A p, (p ≥ 1), then log(w) ∈ BMO (i.e. log(w) has bounded mean oscillation).
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
The lattice has vertex types (1 ⁄ 2)(3 3,4 2) + (1 ⁄ 2)(3,4,6,4), while the dual lattice has vertex types (1 ⁄ 15)(4 6)+(6 ⁄ 15)(4 2,5 2)+(2 ⁄ 15)(5 3)+(6 ⁄ 15)(5 2,4). The critical point is where the longer bonds (on both the lattice and dual lattice) have occupation probability p = 2 sin (π/18) = 0.347296... which is the bond ...
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Common to all versions are a set of n items, with each item having an associated profit p j and weight w j. The binary decision variable x j is used to select the item. The objective is to pick some of the items, with maximal total profit, while obeying that the maximum total weight of the chosen items must not exceed W .
At every iteration of Prim's algorithm, an edge must be found that connects a vertex in a subgraph to a vertex outside the subgraph. Since P is connected, there will always be a path to every vertex. The output Y of Prim's algorithm is a tree, because the edge and vertex added to tree Y are connected. Let Y 1 be a